Net Force Problem: Stopping an Auto in 1.8 cm

[Crusaderking1]

Homework Statement

An advertisement claims that a particular automobile can "stop on a dime". What net force would actually be necessary to stop an automobile of mass 850 kg traveling initially at a speed of 51.0 km/h in a distance equal to the diameter of a dime, which is 1.8 cm? Answer must be in two sig. figs.

Homework Equations

V² = u² + 2 a*s
F(net) = m*a

The Attempt at a Solution

51 km/h = 14.16 m/s

0= (14.16)^2 + 2a(0.018)
a= 200.5 / -0.036
a= -5,569.4 m/s^2

850 kg * -5569.4 = Fnet

Fnet = 4,734,027.78 N
(this is 2 sig figs right)?

Did I do this right? If I did, why exactly do I receive -0.036?(I just multiply 0.018 but I don't really understand why.)

Thanks.

 

[AdkinsJr]

Your answer has 2 decimal places. Two sig figs would be 4.7 * 10^6 N. That's probably what they're looking for. You dont' get the negative value from multiplying, that came from solving your equation for "a."

V_o^2=-2a_x\Delta x

 

[Crusaderking1]

Your answer has 2 decimal places. Two sig figs would be 4.7 * 10^6 N. That's probably what they're looking for. You dont' get the negative value from multiplying, that came from solving your equation for "a."

V_o^2=-2a_x\Delta x

Oh ok thanks. I forgot about that notation.

Ok, even without the negative value, the final answer should still be the same right?(positive)

 

[AdkinsJr]

Oh ok thanks. I forgot about that notation.

Ok, even without the negative value, the final answer should still be the same right?(positive)

No, it should be negative because if you're taking the direction of the initial velocity to be in the +x direction (which you are of course) the acceleration is in the opposite (negative) direction because it is bringing the car to a stop. For the force, you wrote:

850 kg * -5569.4 = Fnet

This is correct, but you have to keep the negative when you multiply. You're multiplying a negative and a positive, the result is -4.7*10^6 N

 

[Crusaderking1]

No, it should be negative because if you're taking the direction of the initial velocity to be in the +x direction (which you are of course) the acceleration is in the opposite (negative) direction because it is bringing the car to a stop. For the force, you wrote:

850 kg * -5569.4 = Fnet

This is correct, but you have to keep the negative when you multiply. You're multiplying a negative and a positive, the result is -4.7*10^6 N

Thanks for the clarification. Much appreciated.